Ultra-precision machining is dominated by single-crystal diamond cutting tools, and is typically applied to a narrow range of materials, particularly aluminum and copper. Single-crystal SiC can be comparable to some diamonds in hardness and thermal conductivity, while potentially having superior chemical and thermal stability, yet it has not been explored as a cutting tool for ultra-precision machining. We made two cutting tools with single-crystal SiC, one with sharp corners and one with a large circular radius, and used them to cut flat surfaces on two materials, 316 stainless steel and nickel. These materials generally cause unacceptably rapid diamond tool wear. We report the average roughness of the resulting surfaces cut with single-crystal 4H and 6H SiC tools.